Rep:Mod:Jkt115

NH3

Summary Analysis

Method: RB3LYP

Basis set: 6-31G(d,p)

E(RB3LYP): -56.55776873 au

RMS Gradient: 0.00000485 au

Point Group: C3V

N-H: 1.01798 A

H-N-H: 105.741 degrees

         Item               Value     Threshold  Converged?
 Maximum Force            0.000004     0.000450     YES
 RMS     Force            0.000004     0.000300     YES
 Maximum Displacement     0.000072     0.001800     YES
 RMS     Displacement     0.000035     0.001200     YES

Ammonia NH3

The optimisation file is linked to here

Frequency Analysis

The different vibration modes of NH3.

How many modes do you expect from the 3N-6 rule? (3x4)-6=6

Which modes are degenerate? 2,3 and 5,6

Which modes are "bending" vibrations and which are "bond stretch" vibrations? Bending: 1, 2 and 3 Bond Stretch: 4, 5 and 6

Which modes is highly symmetric? 1 and 4

One mode is known as the "umbrella" mode, which one is this? Mode 1

How many bands would you expect to see in an experimental spectrum of gaseous ammonia? 2 bands because modes 4-6 has an infra-red value that will be too small to be visible.

Charge of N: -1.125

Charge of H: 0.375

I would expect the charge on the nitrogen to be negative and the charge of the hydrogen to be positive. This is because nitrogen is more electronegative than hydrogen, therefore, electron density will be pulled towards the nitrogen nuclei.

N2

Summary Analysis

Method: RB3LYP

Basis set: 6-31G(d,p)

E(RB3LYP): -109.52412868 au

RMS Gradient: 0.00000060 au

Point Group: D∞h

N-N distance: 1.10550 A

N-N angle: 180 degrees

Charge of N: 0 because it is an homonuclear molecule.

         Item               Value     Threshold  Converged?
 Maximum Force            0.000001     0.000450     YES
 RMS     Force            0.000001     0.000300     YES
 Maximum Displacement     0.000000     0.001800     YES
 RMS     Displacement     0.000000     0.001200     YES

Nitrogen N2

The optimisation file is linked to here

Frequency Analysis

The vibration mode of N2. There is only 1 vibrational mode because of the 3N-5 rule: (3*2)-5 = 1

H2

Summary Analysis

Method: RB3LYP

Basis set: 6-31G(d,p)

E(RB3LYP): -1.17853936 au

RMS Gradient: 0.00000017 au

Point Group: D∞h

H-H distance: 0.74279 A

H-H angle: 180 degrees

Charge of H: 0 because it is a homonuclear molecule.

         Item               Value     Threshold  Converged?
 Maximum Force            0.000000     0.000450     YES
 RMS     Force            0.000000     0.000300     YES
 Maximum Displacement     0.000000     0.001800     YES
 RMS     Displacement     0.000001     0.001200     YES

Hydrogen H2

The optimisation file is linked to here

Frequency Analysis

The vibration mode of H2. There is only 1 vibrational mode because of the 3N-5 rule: (3*2)-5 = 1

Haber-Bosch process

N2 + 3H2 -> 2NH3

E(NH3)= -56.55776873 au

2*E(NH3)= 2*-56.55776873= -113.11553746 au

E(N2)= -109.52412868 au

E(H2)= -1.17853936 au

3*E(H2)= 3*-1.17853936= -3.53561808 au

ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.0557907 au = -146.48 kJ/mol

The ammonia product is more stable than the gaseous reactants.

H2O

Summary Analysis

Method: RB3LYP

Basis set: 6-31G(d,p)

E(RB3LYP): -76.41973740 au

RMS Gradient: 0.00006276 au

Point Group: C2V

O-H distance: 0.96522 A

H-H angle: 103.745 degrees

         Item               Value     Threshold  Converged?
 Maximum Force            0.000099     0.000450     YES
 RMS     Force            0.000081     0.000300     YES
 Maximum Displacement     0.000115     0.001800     YES
 RMS     Displacement     0.000120     0.001200     YES

Water H2O

The optimisation file is liked to here

Frequency Analysis

The different vibration modes of H2O. There is only 3 vibrational mode because of the 3N-6 rule: (3*3)-6 = 3

Charge of O: -0.944

Charge of H: 0.472

The following MO diagrams are based on this orientation of H2O.

3D axis.

This is a bonding MO that is made by the constructive overlap of the 2s orbital from O and the 1s orbital from the two H's. This MO is occupied and has a low energy. This MO is responsible for the two sigma bonds.

This is a bonding MO that is made by the constructive overlap of the 2px orbital from O and the 1s orbital from the two H's. This MO is occupied and has an energy in the HOMO/LUMO region. This MO is responsible for the two sigma bonds.

This is a bonding MO that is made by the constructive overlap of the 2py orbital from O and the 1s orbital from the two H's. This MO is occupied and has an energy in the HOMO/LUMO region. This MO is responsible for the two sigma bonds.

This is an anti-bonding MO that is made by the destructive overlap of the 2pz orbital from O and the 1s orbital from the two H's. This MO is unoccupied and has an energy in the HOMO/LUMO region.

This is an anti-bonding MO that is made by the destructive overlap of the 2px orbital from O and the 1s orbital from the two H's. This MO is unoccupied and has an energy in the HOMO/LUMO region.

Electrolysis of Water

2H2O -> 2H2 + O2

E(H2O)= -76.41973740 au

2*E(H2O)= 2*-76.41973740= -152.8394748 au

E(H2)= -1.17853936 au

2*E(H2)= 2*-1.17853936= -2.35707872 au

E(O2)= -150.25742434 au

ΔE= [(2*E(H2))+E(O2)]-[2*E(H2O)]= 0.22497174 au = +590.66 kJ/mol